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Q1. Simplify

• 1) 5 t⁴
• 2) 3 t³
• 3) 5 t³
• 4) 3 t⁵

Solution

Q2. Simplify:

Solution

Q3. Compare the following pair of numbers. (i) 2.5 x 10³ and 3.5 x 10² (ii) 2⁵ and 5²

Solution

(i) 2.5 x 10³ and 3.5 x 10² Or, 2.5 x 1000 and 3.5 x 100 Or, 2500 and 350 Clearly, 2500 > 350 Therefore, 2.5 x 10³ > 3.5 x 10² (ii) 2⁵ and 5² Or, 2 x 2 x 2 x 2 x 2 and 5 x 5 Or, 32 and 25 Clearly, 32 > 25 Therefore, 2⁵ > 5²

Q4.

• 1)
• 2) _2¹⁵
• 3)
• 4)

Solution

Q5. a × a × a × a × y × y × y × y × z × z can be written as

• 1) a⁴y⁴z²
• 2) ay⁸xz²
• 3) ayz¹⁰
• 4) ayz⁸

Solution

a × a × a × a × y × y × y × y × z × z = a⁴y⁴z²

Q6. The product 108144 expressed as product of prime factors is

• 1) 2⁵ 3⁶
• 2) 2⁸ 3⁵
• 3) 3⁷ 2⁶
• 4) 2⁶ 3⁵

Solution

The product 108144 can be expressed as 108144 = 12 9 12 12 =2² 3 3² 2² 3 2² 3= 2⁶ 3⁵ .....Rearranging and adding the powers of prime factors

Q7. Simplify:

Solution

Q8. Express the number 451900000 in the form K x 10ⁿ (where K is a number and n is a integer) in 4 different ways.

Solution

Here the number is: 451900000 This can be written as 4519 x 100000 So the 4 different ways are: 4519 x 10⁵, 451.9 x 10⁶, 45.19 x 10⁷, 4.519 x 10⁸

Q9. Simplify:

Solution

Q10. Mass of earth is approximately 5,970,000,000,000,000,000,000,000 kg. Express this mass in standard form.

Solution

Mass of earth = 5,970,000,000,000,000,000,000,000 kg = 597 x 10000000000000000000000 kg = 597 x 10²² kg = 5.97 x 10²⁴ kg

Q11. If 5^{2x + 1} 25 = 125, find the value of x.

Solution

We have, Since bases are equal, powers are also equal.